I put a shortcut to PE in my startup folder and set it to run as a minimized window. This works, but I get the icon in the task bar and program group in the task bar. When I restore it and minimize it again I just get the tray icon.

Just out of curiosity:
did you specify PE to run minimized by some feature of your OS (which is ...?) or by some feature of PE itself.
I've just searched through all the PE documentation and didn't find any reference to it, so if there isn't any: How about a commandline option to run PE minimized to the tray?